A process of this type is known from U.S. Pat. No. 5,059,735. In this process, a large amount of propane (a C.sub.3 -alkane) is added to the feed mixture containing C.sub.4 -olefins to C.sub.7 -olefins before it is passed over the catalyst, and in addition to C.sub.2 -olefins to C.sub.4 -olefins a considerable amount of C.sub.6 and higher aromatics is generated.